Imagine yourself on a game show looking at three identical doors. Behind two doors lie useless goats. One Door, however, houses a new car. You are to choose one of the three doors. Following your decision, the host of the game show then opens a door which contains a goat and gives you a choice: do you wish to stay on your previously selected door or switch to the remaining one. What do you do?

Generally, one's first instinct is to say that it does not matter. Statistically, each door has a 50% chance of containing either the car or the goat. However, one's first instinct is wrong.

Let's imagine that instead of three doors, we have 100. You choose one door, meaning that you have a 1/100 chance of getting the car, or a one percent chance. So, the host then picks 98 doors that do NOT contain the car, leaving you with two left. Your door was picked with a 1/100 chance and that does not change. There were 99 other doors that you could have picked. Now, 98 of those doors have been taken out of the game, leaving the remaining door with a 99 percent chance of containing the car.

Going back to the three doors, switching will always improve one's odds of winning. The first choice has a 1/3 chance and the switch has a 2/3 chance of containing the car. Another way of viewing this paradox is via the following set of paths that can happen (knowing that the host will NEVER pick the door with the car):

You choose goat one - Host opens goat 2 - Switch = Win
You chose goat two - Host opens goat 1 - Switch = Win
You chose car - Host opens either goat 1 or 2 - Switch = Loss

When given a scenario similar to the Monty Hall Paradox, always remember to switch!